Multi-cluster crack competitive expansion discrete element simulation method and quantitative evaluation method

Abstract

The invention discloses a multi-cluster crack competitive extension discrete element simulation method and a quantitative evaluation method, and relates to the technical field of oil and gas reservoir exploitation, the method comprises the following steps: obtaining geological parameters of a target reservoir, rock mechanics parameters, shaft parameters of a target well, engineering parameters in fracturing transformation, and fluid parameters of a used fluid; establishing a shaft friction calculation model; establishing a perforation hole abrasion correction model; establishing a dynamic shaft flow distribution model; discrete element simulation is conducted on the dynamic wellbore flow distribution model, the hole diameter, the flow coefficient and the final flow change curve are obtained through iterative calculation, and the variable coefficient is obtained. According to the method, the flow distribution and crack expansion process under the complex reservoir condition can be more accurately simulated, and the scientificity and field applicability of hydraulic fracturing design are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas reservoir exploitation, and particularly relates to a discrete element simulation method and a quantitative evaluation method for multi-cluster fracture competitive propagation based on dynamic flow allocation. Background Art

[0002] With the continuous development of horizontal well technology and the continuous increase of China's external oil and gas dependence, strengthening the exploration and development of deep unconventional oil and gas reservoirs has become the key path to reduce external dependence. Unconventional oil and gas resources in China are widely distributed, with complex sedimentary environments, strong reservoir heterogeneity, developed horizontal bedding and natural fractures, and complex stress fields. Traditional development simulation methods, such as the finite element method and the boundary element method, are difficult to effectively handle heterogeneous media, especially unable to couple a large number of randomly distributed natural fractures. Therefore, research based on the discrete element method has significant advantages in the application of weak-plane developed and discontinuous media such as shale and carbonate rocks. The discrete element method can more realistically reflect the mechanical response behavior of rocks under complex conditions and is an ideal tool for simulating hydraulic fracturing.

[0003] However, currently in the application of the discrete element method, the coupled simulation of flow allocation is still less. Existing patents and papers usually only consider a few influencing factors and ignore the multiple coupled effects such as wellbore friction, perforation hole erosion, and fracture closure pressure, resulting in a large deviation between the simulation results and the actual field situation. Especially in the process of multi-cluster fracture propagation, the flow competition relationship between fractures has an important impact on the final fracture morphology and stimulation effect. Implementing the coupled simulation of flow allocation through the discrete element method can more realistically reflect the synchronous propagation process of multi-cluster fractures in complex reservoirs, quantitatively evaluate the fracture propagation uniformity and flow allocation law, and then optimize the hydraulic fracturing plan. Summary of the Invention

[0004] In view of the above problems, the present invention aims to provide a discrete element simulation method and a quantitative evaluation method for multi-cluster fracture competitive propagation based on dynamic flow allocation. This method is based on the discrete element method for multi-cluster fracture competitive propagation and flow allocation coupled simulation and quantitative evaluation method, considering the wellbore friction of commonly used slickwater fracturing fluid in the construction site, perforation hole erosion, and the flow allocation situation caused by the in-fracture closure pressure, and quantitatively judging the fracture propagation uniformity, which can more realistically reflect the synchronous propagation process of multi-cluster fractures in complex reservoirs, quantitatively evaluate the fracture propagation uniformity and flow allocation law, and then optimize the hydraulic fracturing plan.

[0005] The technical solution provided by the present invention to solve the above technical problems is: A discrete element simulation method for multi-cluster fracture competitive propagation based on dynamic flow allocation, comprising the following steps:

[0006] Obtain the geological parameters, rock mechanical parameters of the target reservoir, wellbore parameters of the target well, engineering parameters in the fracturing transformation, and fluid parameters of the used fluid;

[0007] Obtain the rheological properties of the power-law fluid according to the fluid parameters; establish a wellbore friction calculation model based on the rheological properties of the power-law fluid, wellbore parameters, and engineering parameters;

[0008] Conduct indoor simulation experiments according to the fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, and establish a perforation hole erosion correction model;

[0009] Establish a reservoir geological model according to the geological parameters and rock mechanical parameters of the target reservoir, and obtain the hydraulic fracture closure pressure according to the reservoir geological model; and based on Kirchhoff's law, establish a dynamic wellbore flow rate distribution model according to the wellbore friction calculation model, perforation hole erosion correction model, and hydraulic fracture closure pressure;

[0010] Conduct discrete element simulation on the dynamic wellbore flow rate distribution model, and iteratively calculate to obtain the hole diameter, flow coefficient, final flow rate change curve, and obtain the coefficient of variation.

[0011] Further, in some embodiments of the present application, the coefficient of variation CV is:

[0012]

[0013] In the formula, k is the number of fracture clusters; n i is the number of flow rate changes of fracture cluster i, x ij is the flow rate value of fracture cluster i at different times, and j is the index of flow rate change.

[0014] Further, in some embodiments of the present application, the geological parameters include: reservoir thickness, interlayer thickness, bedding joint density; the rock mechanical parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, vertical stress;

[0015] The engineering parameters include: number of clusters, cluster spacing, number of perforations, hole diameter, initial hole flow coefficient, maximum hole flow coefficient, displacement;

[0016] The fluid parameters include: concentration, viscosity, density, bulk modulus, shear rate;

[0017] The wellbore parameters include: wellbore diameter.

[0018] Further, in some embodiments of the present application, the rheological properties of the power-law fluid include the flow behavior index and consistency coefficient, and the flow behavior index and consistency coefficient are obtained by fitting the shear rate and viscosity;

[0019] The fitting equation for shear rate and viscosity is as follows:

[0020] η = K·γ n-1 (2)

[0021] Where: η is viscosity, Pa·s; K is consistency coefficient, Pa·s n ; γ is shear rate, s -1 ; n is flow pattern coefficient.

[0022] Furthermore, in some embodiments of the present application, the wellbore friction calculation model is:

[0023]

[0024] Where: Δp pp is the wellbore flow friction, Pa; ρ is fluid density, kg / m 3 ; v is the flow velocity in the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s is the pipe friction coefficient; f is the friction coefficient along the way; A, B are calculation parameters of the friction coefficient along the way; K is the consistency coefficient, Pa·s n ; n is the flow pattern coefficient.

[0025] Furthermore, in some embodiments of the present application, the perforation hole erosion correction model is:

[0026]

[0027] Where: Δp pf is the hole friction, Pa; Q i is the displacement corresponding to fracture cluster i, m 3 / s; N is the number of perforation holes, and i is the cluster number of the fracture.

[0028] Furthermore, in some embodiments of the present application, according to fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, an indoor simulation experiment is carried out to establish a perforation hole erosion correction model, including the following steps:

[0029] According to the above-mentioned concentration of proppant and reservoir parameters, wellbore parameters, and engineering parameters, an indoor simulation experiment is carried out, and the concentration, injection speed, and time of the injected proppant are adjusted to simulate the influence of the concentration, injection speed, and time of the proppant on the degree of hole erosion, and data of different proppant injection speeds, times, and their corresponding perforation hole diameters are obtained, and linear relationship fitting is carried out to obtain perforation erosion parameters, and its fitting relation formula is as shown in (5):

[0030]

[0031] Where: d t+ΔtWith d t are the perforation hole diameters at times t + Δt and t, respectively, in m; α and β are the empirical coefficients obtained from linear fitting, in (m 2 ·s) / kg and (m·s) / kg; v p is the flow velocity of the fluid in the hole, in m / s; Cd t+Δt 、Cd t and Cd max are the maximum flow coefficients at times t + Δt, t, and respectively; C is the proppant concentration, in kg / m 3 ;

[0032] According to (5), the equation for the real-time perforation friction is obtained, which is the perforation hole abrasion correction model.

[0033] Furthermore, in some embodiments of the present application, the dynamic wellbore flow distribution model is:

[0034]

[0035] Where: p cp,i is the closure pressure of fracture cluster i, in Pa.

[0036] Furthermore, in some embodiments of the present application, the establishment of the dynamic wellbore flow distribution model is as follows:

[0037] Let the total flow equivalent pressure drop Δp i of the i-th cluster of fractures be:

[0038]

[0039] Where: Δp f,i is the perforation pressure drop of fracture cluster i, in Pa; Δp pp,i is the wellbore friction pressure drop of fracture cluster i, k is the total number of fracture clusters, i is the number of the fracture cluster, and its value ranges from 1 to k;

[0040] The Δp i calculated according to the above formula is then substituted into the following formulas (8) and (9):

[0041] r i = Δp i / q i (8)

[0042]

[0043] Where: q i is the flow rate of fracture cluster i, in m 3 / s; r t is the equivalent friction, in Pa;

[0044] The flow rate q of fracture cluster i can be obtainedi The calculation formula is the dynamic wellbore flow rate allocation model.

[0045] This application also provides a quantitative evaluation method for engineering parameters in hydraulic fracturing. By using the above multi-cluster fracture competition and propagation discrete element simulation method, the propagation morphology and flow rate allocation of multi-cluster fractures under different engineering parameter conditions are obtained, and the corresponding engineering parameters are evaluated according to the obtained propagation morphology and flow rate allocation of multi-cluster fractures.

[0046] A further technical solution is that in step 7, the real-time calculation of the single-cluster closure pressure, the degree of hole abrasion, and the monitoring of the change in the single-cluster flow rate are carried out, and the coefficient of variation of the final result is quantitatively evaluated.

[0047] The single-cluster closure pressure is calculated in real time, the flow plane area and sub-contact are recorded in real time, and the hydraulic fracture closure pressure is calculated through the sub-contact reaction force and returned to the flow rate allocation model in real time to participate in the calculation of flow rate allocation iteration.

[0048] Record the hole diameter, flow coefficient, and stable flow rate after iteration, input the required parameters into the model again, and perform the calculation for the next time step until the pumping time of this stage.

[0049] By deriving the hole diameter, flow coefficient, and final flow rate change curve, calculate the coefficient of variation under different parameters. The formula is:

[0050]

[0051] In the formula, k is the number of fracture clusters; n i is the number of flow rate changes of fracture cluster i, and x ij is the flow rate value of fracture cluster i at different times.

[0052] Evaluate the uniformity of flow rate allocation of each cluster in different situations by comparing the flow rate coefficient of variation CV under different geological and engineering parameters.

[0053] The beneficial effects of the present invention: Based on the discrete element method, the present invention proposes a multi-cluster fracture propagation model and a quantitative evaluation method that comprehensively consider hole abrasion, the frictional resistance of power-law fluid along the wellbore, and the closure pressure in the fracture. It is more suitable for shale reservoirs, which are discontinuous media with a large number of discrete fractures, improves the accuracy of multi-cluster fracture morphology prediction, and is used for hydraulic fracturing simulation and optimization of engineering parameters under various conditions, which is more in line with the actual engineering needs. Description of the Drawings

[0054] Figure 1 It is a schematic diagram of the multi-cluster flow rate allocation process during the whole process of hydraulic fracturing;

[0055] Figure 2 It is a diagram of the experimental results of power-law fluid in the laboratory with polyacrylamide as an example;

[0056] Figure 3 It is a real-time change diagram of the diameter of each cluster of perforations;

[0057] Figure 4 It is a real-time change diagram of the flow rate of each cluster;

[0058] Figure 5 Flow difference coefficient diagram under different parameters;

[0059] Figure 6 It is a multi-cluster fracture propagation morphology diagram under different parameters. Among them, (a) is the multi-cluster fracture propagation morphology diagram with an upper barrier layer developed, (b) is the multi-cluster fracture propagation morphology diagram with a lower barrier layer developed, and (c) is the multi-cluster fracture propagation morphology diagram with both upper and lower barrier layers developed. Specific implementation manners

[0060] Next, the technical solutions of the present application will be clearly and completely described in conjunction with the embodiments. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0061] The embodiments of the present application provide a discrete element simulation method for multi-cluster fracture competitive propagation, including:

[0062] Obtain the geological parameters, rock mechanical parameters of the target reservoir, wellbore parameters of the target well, engineering parameters in the fracturing transformation, and fluid parameters of the used fluid;

[0063] Obtain the rheological properties of the power-law fluid according to the fluid parameters; establish a wellbore friction calculation model according to the rheological properties of the power-law fluid, wellbore parameters, and engineering parameters;

[0064] Conduct indoor simulation experiments according to the fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, and establish a perforation abrasion correction model;

[0065] Establish a reservoir geological model according to the geological parameters and rock mechanical parameters of the target reservoir. According to the reservoir geological model and Kirchhoff's law, establish a dynamic wellbore flow rate distribution model according to the wellbore friction calculation model, perforation abrasion correction model, and hydraulic fracture closure pressure;

[0066] Perform discrete element simulation on the dynamic wellbore flow rate distribution model, and iteratively calculate to obtain the perforation diameter, flow coefficient, final flow rate change curve, and obtain the coefficient of variation.

[0067] Among them, Kirchhoff's law is the basic law followed by voltage and current in an electric circuit. Here, the pressure drop is analogized to voltage and the flow rate is analogized to current to establish a flow rate distribution model.

[0068] Among them, the calculation formula of the coefficient of variation CV is as follows:

[0069]

[0070] In the formula, k is the number of fracture clusters; n i is the number of flow rate changes of fracture cluster i, x ij is the flow rate value of fracture cluster i at different times, i is the number of the fracture cluster; j is the index of the flow rate change.

[0071] By calculating the overall coefficient of variation in different cases, the difference in flow rate distribution under different engineering parameters or geological parameters is evaluated. If the coefficient of variation is large, it indicates that some fracture clusters have not been effectively extended. For example: when the coefficient of variation ≥ 10%, it indicates that some fractures in the reservoir have not been effectively extended; when the coefficient of variation ≤ 10%, it indicates that the fractures in the reservoir have been fully extended, the corresponding engineering parameters are better, and the flow rate distribution is balanced.

[0072] Among them, the geological parameters include: reservoir thickness, interlayer thickness, bedding joint density; the rock mechanical parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, vertical stress;

[0073] The engineering parameters include: number of clusters, cluster spacing, number of perforations, hole diameter, initial flow coefficient of the hole, maximum flow coefficient of the hole, displacement;

[0074] The fluid parameters include: concentration, viscosity, density, bulk modulus, shear rate;

[0075] The wellbore parameters include: wellbore diameter.

[0076] Among them, the geological parameters and rock mechanical parameters can be obtained through logging data or laboratory experiments on core samples, such as core sample displacement experiments, etc. The engineering parameters can be obtained through engineering data, the fluid parameters can be obtained through laboratory experiments, such as fluid viscosity and rheology measurement experiments, etc., and the wellbore parameters can be obtained through engineering data.

[0077] Among them, the reservoir geological model is a hydraulic fracturing model based on the discrete element method. This model is not a mathematical model but a simulation model. Each parameter in it is obtained through experiments or logging, which can reflect the in-situ geomechanical characteristics of the reservoir under real conditions and is used for hydraulic fracturing simulation. The method for establishing it is prior art, and reference can be made to the method for establishing the reservoir geological model recorded in (Huang T, Zhong Y, Mou Q, et al. Discrete element method simulation of competitive fracture propagation in staged multi-cluster fracturing in shale oil reservoirs[J]. Bulletin of Engineering Geology and the Environment, 2024, 83(10): 1-13.) to establish it.

[0078] In addition, the fracture propagation patterns include single fractures, complex fractures, natural fracture opening fractures, complex fracture networks, deflected fractures, etc., which are classified by the fracture mode and propagation path. In this application, the reservoir geological model is also used to judge the fracture propagation pattern after the reservoir is fractured. The specific judgment method is as follows: through the discrete element model, analyze the sub-contact failure mode, quantify the proportion of failure types, and directly observe the overall fracture morphology. A power-law fluid refers to a fluid that conforms to the rheological law of τ = K * γ^n.

[0079] Among them, τ - shear stress

[0080] K - consistency coefficient, or called power-law coefficient, unit: Pa·sn

[0081] n - flow behavior index, or called power-law index, dimensionless

[0082] The value of K is a measure of viscosity, but it is not equal to the viscosity value. The higher the viscosity, the higher the value of K.

[0083] Within a certain range of shear rate, the value of n can be treated as a constant.

[0084] The value of n is a measure of non-Newtonian behavior. The lower or higher the value of n, the more curved the curve, and the stronger the non-Newtonian behavior. Generally, the value of n for mud is preferably below 0.5.

[0085] During the process of oil and gas development, the slickwater used for fracturing is a power-law fluid, so its consistency coefficient and flow behavior index (flow pattern coefficient) can also be obtained by using the above calculation formula.

[0086] Specifically as follows: The flow pattern coefficient and consistency coefficient of the slickwater are obtained by fitting the shear rate and viscosity;

[0087] The fitting equation for shear rate and viscosity is as follows:

[0088] η = K·γ n-1 (2)

[0089] Where: η is the viscosity, Pa·s; K is the consistency coefficient, Pa·s n ; γ is the shear rate, s -1 ; n is the flow behavior index.

[0090] Based on the above parameters, considering the flow characteristics of power-law fluid in the wellbore, a wellbore friction calculation model is established. The wellbore friction calculation model is as follows:

[0091]

[0092] Where: Δp pp is the wellbore flow friction, Pa; ρ is the fluid density, kg / m 3 ; v is the flow velocity in the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s is the pipe friction coefficient; f is the friction factor along the path; A, B are the calculation parameters of the friction factor along the path; K is the consistency coefficient, Pa·s n ; n is the flow behavior index.

[0093] Then, according to the fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, an indoor simulation experiment is carried out to establish a perforation hole erosion correction model, including the following steps:

[0094] According to the concentration of the above proppant, reservoir parameters, wellbore parameters, and engineering parameters, an indoor simulation experiment is carried out, and the concentration, injection rate, and time of the injected proppant are adjusted to simulate the influence of the concentration, injection rate, and time of the proppant on the degree of hole erosion, and the data of different proppant injection rates, times, and their corresponding perforation hole diameters are obtained. Linear relationship fitting is carried out to obtain the perforation erosion parameters, and the fitting relationship formula is as shown in (5):

[0095]

[0096] Where: d t+Δt and d t are the perforation hole diameters at time t + Δt and time t respectively, m; α and β are the empirical coefficients obtained by linear fitting, (m 2 ·s) / kg and (m·s) / kg; v p is the flow velocity of the fluid in the hole, m / s; Cd t+Δt , Cd t and Cd max are the maximum flow coefficients at time t + Δt, time t and maximum flow rate respectively; C is the proppant concentration, kg / m3 。

[0097] According to (5), the equation for real-time perforation friction is obtained, which is the perforation hole erosion correction model. The perforation hole erosion correction model is as follows:

[0098]

[0099] In the formula: Δp pf is the hole friction, Pa; Q i is the displacement corresponding to fracture cluster i, m 3 / s; N is the number of perforation holes, and i is the number of the fracture cluster.

[0100] For the discrete element simulation of the reservoir geological model, as the fracturing process progresses, the state of the reservoir geological model is updated in real time. The grid nodes in the reservoir geological model are traversed to calculate the reaction force of hydraulic fracturing on the wall surface and divide it by the open fracture area to obtain the hydraulic fracture closure pressure. Based on Kirchhoff's law, the hydraulic fracture closure pressure is coupled into the above perforation hole erosion correction model to establish a dynamic wellbore flow rate distribution model. The process is as follows:

[0101] Let the total flow equivalent pressure drop Δp i of the i-th fracture cluster be:

[0102]

[0103] In the formula: Δp f,i is the perforation pressure drop of fracture cluster i, Pa; Δp pp,i is the wellbore friction pressure drop along the way of fracture cluster i. i is the number of the fracture cluster and takes values in the range of 1 to k;

[0104] According to the above formula, the calculated Δp i , and then substitute it into the following formulas (8) and (9):

[0105] r i = Δp i / q i (8)

[0106]

[0107] In the formula: q i is the flow rate of fracture cluster i, m 3 / s; r t is the equivalent friction, Pa;

[0108] Then the calculation formula for the flow rate q i of fracture cluster i can be obtained, which is the dynamic wellbore flow rate distribution model. The dynamic wellbore flow rate distribution model is as follows:

[0109]

[0110] Where: p cp,i is the closure pressure of fracture cluster i, in Pa.

[0111] After obtaining the above dynamic wellbore flow rate distribution model, the single-cluster closure pressure of the fracture clusters is obtained through real-time detection, iterated until the flow rate of each cluster converges, and the flow rate qi of fracture cluster i is simulated and calculated i , until reaching the proppant-carrying fluid stage, the hole diameter, flow coefficient, and final flow rate change curve are derived, and then the coefficient of variation can be calculated. Based on the coefficient of variation, hydraulic fracturing simulation and engineering parameter optimization are carried out to make it more in line with the actual engineering needs.

[0112] The present application also provides a method for quantitatively evaluating engineering parameters for hydraulic fracturing. By using the above multi-cluster fracture competition and propagation discrete element simulation method, the propagation morphology and flow rate distribution of multi-cluster fractures under different engineering parameter conditions are obtained, and the corresponding engineering parameters are evaluated based on the obtained propagation morphology and flow rate distribution of multi-cluster fractures.

[0113] The following takes the Jimusa'er shale oil reservoir as an example to exemplarily illustrate a multi-cluster fracture competition and propagation discrete element simulation method and a quantitative evaluation method based on dynamic flow rate distribution provided by the present application. Refer to Figure 1 , which is specifically as follows:

[0114] Step 1: Obtain the geological parameters, rock mechanics parameters, wellbore parameters of the target well, engineering parameters in the fracturing transformation, and fluid parameters of the fluid used for the target reservoir;

[0115] The geological parameters include: reservoir thickness, interlayer thickness, bedding fracture density; the rock mechanics parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, vertical stress;

[0116] The engineering parameters include: number of clusters, cluster spacing, number of perforations, hole diameter, initial hole flow coefficient, maximum hole flow coefficient, displacement;

[0117] The fluid parameters include: proppant concentration, fracturing fluid viscosity, fracturing fluid density, fracturing fluid bulk modulus;

[0118] The wellbore parameters include: wellbore diameter.

[0119] The obtained parameters are shown in Table 1.

[0120] Table 1 Simulation parameter table

[0121]

[0122]

[0123] Obtain the rheological properties of power-law fluids such as slickwater, such as shear rate and viscosity, and fit the flow pattern coefficient and consistency coefficient of the power-law fluid according to Equation (1):

[0124] η=K·γ n-1 (2)

[0125] Where: η is the viscosity, Pa·s; K is the consistency coefficient, Pa·s n ; γ is the shear rate, s -1 ; n is the flow pattern coefficient.

[0126] Based on the above parameters, consider the flow characteristics of the power-law fluid in the wellbore to establish a wellbore friction calculation model. The established wellbore module calculation model is shown in (2):

[0127]

[0128] Where: Δp pp is the wellbore flow friction, Pa; ρ is the fluid density, kg / m 3 ; v is the flow velocity in the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s is the pipe friction coefficient.

[0129] According to the above proppant concentration, reservoir parameters, wellbore parameters, and engineering parameters, conduct indoor simulation experiments, and adjust the concentration, injection rate, and time of the injected proppant to simulate the influence of the proppant concentration, injection rate, and time on the perforation erosion degree. Obtain the data of different proppant injection rates, times, and their corresponding perforation hole diameters, and conduct a linear relationship fitting to obtain the perforation erosion parameters. The fitting relationship formula is shown in (3):

[0130]

[0131] Where: d t+Δt and d t are the perforation hole diameters at t+Δt and t moments, m; α and β are the empirical coefficients obtained by linear fitting, (m 2 ·s) / kg and (m·s) / kg; v p is the flow velocity of the fluid in the hole, m / s; Cd t+Δt , Cd t and Cd max are the maximum flow coefficients at t+Δt, t, and the maximum flow coefficient respectively.

[0132] The real-time perforation friction is obtained from the above formula as:

[0133]

[0134] Where: Δppf is the perforation friction, Pa; Q i is the displacement of fracture cluster i, m 3 / s; N is the number of perforation holes.

[0135] For the discrete element simulation of the reservoir geological model, as the fracturing process progresses, the state of the reservoir geological model is updated in real time. The grid nodes in the reservoir geological model are traversed to calculate the reaction force of hydraulic fracturing on the wall surface and divided by the open fracture area to obtain the hydraulic fracture closure pressure. And based on Kirchhoff's law, a dynamic wellbore flow rate distribution model is established by coupling the hydraulic fracture closure pressure. The specific establishment process is as follows:

[0136] Taking the heel end as fracture cluster 1 and the toe end as fracture cluster 5 as an example, the total flow equivalent pressure drop Δp of the i-th cluster i is:

[0137]

[0138] In the formula: Δp f,i is the perforation pressure drop of fracture cluster i, Pa; Δp pp,i is the wellbore friction pressure drop of fracture cluster i. k is the total number of fracture clusters, and i is the number of fracture clusters, which takes values in the range of 1 to k.

[0139] The Δp calculated according to the above formula i , and then substituted into the following formulas (6) and (7). The formulas (6) and (7) are:

[0140] r i = Δp i / q i (7)

[0141]

[0142] In the formula: q i is the flow rate of fracture cluster i, m 3 / s; r t is the equivalent friction, Pa.

[0143] The flow rate q of fracture cluster i can be obtained i The calculation formula is shown in formula (8), which is the dynamic wellbore flow rate distribution model:

[0144]

[0145] In the formula: p cp,i is the closure pressure of fracture cluster i, Pa.

[0146] The loop solution for this step is carried out by the Newton iteration algorithm until the equation converges to obtain the stable convergence flow rate. The above model is subjected to full-coupling analysis through discrete element hydraulic fracturing simulation, and the single-cluster closure pressure and model state are monitored in real time. The perforation hole erosion degree, the change of single-cluster flow rate are quantitatively compared, and the flow rate distribution uniformity and propagation morphology of multi-cluster fractures are quantitatively evaluated through the coefficient of variation.

[0147] The specific steps are as follows: Select the constitutive model required for discrete element simulation, taking the Mohr-Coulomb strength criterion as an example:

[0148]

[0149] In the formula: T f is the tensile strength, Pa; S f is the peak shear strength, Pa; c is the cohesion, Pa; σ n is the normal stress, Pa; is the internal friction angle, °.

[0150] The fluid-solid coupling model in discrete element is:

[0151]

[0152] In the formula: u h0 is the initial opening, m; Δu m is the opening change, m; f is the correction factor; Q is the flow velocity, m 3 / s; u m is the boundary distance, m; ρ is the fluid density, kg / m 3 ; g is the acceleration of gravity, m / s 2 ; μ is the fluid viscosity Pa·s; K H is the water head, m.

[0153] The detailed process of the multi-cluster fracture competition propagation simulation by the discrete element method is as follows: Preset the flow rate of each cluster to 3.2 m 3 / min, and perform fluid-solid coupling calculation to verify whether the time reaches the proppant-carrying fluid stage. If not, calculate the frictional resistance along the way, read the closure pressure of the opened fracture, substitute it into the flow rate distribution equation based on Kirchhoff's law, iterate until the flow rate of each cluster converges, update the flow rate parameters, and perform the discrete element fluid-solid coupling calculation for the next time step. Repeat the above steps until the proppant-carrying fluid stage is reached. After reaching the proppant-carrying fluid stage, update the hole diameter and flow coefficient according to the previous time step, calculate the perforation friction and the frictional resistance along the way, read the closure pressure, calculate the comprehensive frictional resistance, substitute it into the flow rate distribution equation based on Kirchhoff's law, iterate until the flow rate of each cluster converges, update the flow rate parameters, and perform the fluid-solid coupling calculation. Repeat the above steps until the simulation time is reached.

[0154] Derive the hole diameter, flow coefficient, and final flow rate change curve from the simulation results, and calculate the coefficient of variation under different parameters. The formula is as follows:

[0155]

[0156] In the formula, k is the number of fracture clusters; n i is the number of flow rate changes of fracture cluster i, and x ij is the flow rate value of fracture cluster i at different times.

[0157] By changing the parameters, calculate the flow rate distribution and fracture propagation morphology under different conditions, which are used for hydraulic fracturing simulation and optimizing engineering parameters to make them more in line with the actual engineering requirements. Refer to Figures 2 to 6 , it can be seen from the figure that the perforation radius shows non-linear growth; in the preflush stage, as the fracturing process progresses, the flow rates of each cluster tend to be evenly distributed. In the proppant-carrying fluid stage, rapid changes occur in the fractures of each cluster, and the dominant fractures appear; as the number of interlayers increases, the coefficient of variation of the flow rate decreases significantly, and the fractures of each cluster tend to develop evenly.

Claims

1. A multi-cluster crack competition expansion discrete element simulation method based on dynamic flow distribution, characterized by: include: Obtain geological parameters of the target reservoir, rock mechanics parameters, wellbore parameters of the target well, engineering parameters in fracturing transformation, and fluid parameters of the used fluid; Obtaining the rheological properties of the power-law fluid according to the fluid parameters; establishing a wellbore friction calculation model according to the rheological properties of the power-law fluid, wellbore parameters, and engineering parameters; According to the fluid parameters, reservoir parameters, wellbore parameters and engineering parameters, indoor simulation experiments are carried out to establish the perforation hole abrasion correction model; According to the geological parameters and rock mechanics parameters of the target reservoir, a reservoir geological model is established. According to the reservoir geological model and Kirchhoff's law, a dynamic wellbore flow distribution model is established according to the wellbore friction calculation model, the perforation hole abrasion correction model and the hydraulic fracture closure pressure; The dynamic wellbore flow distribution model is simulated by discrete element method, and the hole diameter, flow coefficient, final flow change curve are obtained by iterative calculation to obtain the coefficient of variation.

2. According to the method of discrete element simulation of multi-cluster crack competition expansion based on dynamic flow distribution in claim 1, it is characterized in that: The coefficient of variation CV is: Where k is the number of crack clusters; n i is the number of flow changes of fracture cluster i, x ij is the flow value of fracture cluster i at different times; j is the index of flow change.

3. A discrete element simulation method for multi-cluster crack competition expansion according to claim 1, characterized in that: The geological parameters include: reservoir thickness, interlayer thickness, bedding fracture density; the rock mechanics parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, vertical stress; The engineering parameters include: number of clusters, cluster spacing, number of perforations, hole diameter, hole initial flow coefficient, hole maximum flow coefficient, and displacement; The fluid parameters include: concentration, viscosity, density, bulk modulus, and shear rate; The wellbore parameters include: wellbore diameter.

4. A discrete element simulation method for multi-cluster crack competition expansion according to claim 3, characterized in that: The rheological properties of the power-law fluid include a flow pattern coefficient and a consistency coefficient, and the flow pattern coefficient and the consistency coefficient are obtained by fitting the shear rate and the viscosity; The shear rate and viscosity fitting equation is: η=K·γ n-1 (2) Where: η is viscosity, Pa·s; K is consistency coefficient, Pa·s n ; γ is the shear rate, s -1 ; n is the flow pattern coefficient.

5. A discrete element simulation method for multi-cluster crack competition expansion according to claim 4, characterized in that: The wellbore friction calculation model is: Where: Δp pp is the wellbore flow friction, Pa; ρ is the fluid density, kg / m 3 ; v is the flow velocity in the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s is the pipeline friction coefficient; f is the resistance coefficient along the pipeline; A and B are the calculation parameters of the resistance coefficient along the pipeline; K is the consistency coefficient, Pa·s n ; n is the flow pattern coefficient.

6. A discrete element simulation method for multi-cluster crack competition expansion according to claim 4, characterized in that: The perforation hole abrasion correction model is: Where: Δp pf is the hole friction, Pa; Q i is the displacement corresponding to fracture cluster i, m 3 / s; N is the number of perforations, and i is the number of fracture clusters.

7. A discrete element simulation method for multi-cluster crack competition expansion according to claim 6, characterized in that: According to the fluid parameters, reservoir parameters, wellbore parameters and engineering parameters, indoor simulation experiments are carried out to establish a perforation hole abrasion correction model, including the following steps: According to the above proppant concentration and reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were carried out, and the concentration, injection rate, and time of the injected proppant were adjusted to simulate the influence of the proppant concentration, injection rate, and time on the perforation abrasion degree. The data of different proppant injection rates, times, and their corresponding perforation diameters were obtained, and the linear relationship was fitted to obtain the perforation abrasion parameters. The fitting relationship is shown in (5): Where: d t+Δt With d t are the perforation hole diameters at time t+Δt and time t, respectively; α and β are the empirical coefficients obtained by linear fitting, respectively, (m 2 ·s) / kg and (m·s) / kg; v p is the flow rate of the fluid in the hole, m / s; Cd t+Δt 、Cd t with cd max are time t+Δt, time t and maximum flow coefficient respectively; C is the proppant concentration, kg / m 3 ; According to (5), the equation of real-time perforation friction is obtained, which is the perforation hole abrasion correction model.

8. The method for simulating multi-cluster crack competition expansion discrete element according to claim 6, characterized in that: The dynamic wellbore flow distribution model is: Where: p cp,i is the closing pressure of fracture cluster i, Pa.

9. A discrete element simulation method for multi-cluster crack competition expansion according to claim 8, characterized in that: The dynamic wellbore flow distribution model is established as follows: Assume that the overall equivalent pressure drop of the i-th fracture cluster is Δp i for: Where: Δp f,i is the perforation pressure drop of fracture cluster i, Pa; Δp pp,i is the wellbore pressure drop of fracture cluster i, k is the total number of fracture clusters, i is the number of fracture clusters, and its value ranges from 1 to k; According to the above formula, Δp i , and then substitute into the following equations (8) and (9): r i =Δp i / q i (8) Where: q i is the flow rate of fracture cluster i, m 3 / s;r t is the equivalent friction, Pa; The flow rate q of crack cluster i can be obtained i The calculation formula is the dynamic wellbore flow distribution model.

10. A method for quantitative evaluation of engineering parameters for hydraulic fracturing, characterized in that: The multi-cluster fracture competition expansion discrete element simulation method described in any one of claims 1 to 9 is used to obtain the expansion morphology and flow distribution of the multi-cluster fractures under different engineering parameter conditions, and the corresponding engineering parameters are evaluated based on the obtained expansion morphology and flow distribution of the multi-cluster fractures.

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